The measure of <ABD, <DBC and <ABC are 67, 67 and 134 degrees respectively.
<h3>Bisection of angles</h3>
Angles are bisected if they are divided into two equal parts.
If the angle BC bisects <ABC, hence <ABD and <DBC are equal, hence;
2(11x + 23) = <ABC
Given the following parameters
<ABC = 25x + 34
2(11x + 23) = 25x + 34
Expand
22x +46 = 25x + 34
22x-25x = 34 - 46
-3x = -12
x = 4
Determine the measure of the angles
<ABD = 11x + 23 = <DBC
<ABD = 11(4) + 23
<ABD = 44 + 23
<ABD = 67 degrees
<ABC = 2(67)
<ABC = 134 degrees
Hence the measure of <ABD, <DBC and <ABC are 67, 67 and 134 degrees respectively.
Learn more on bisection of angles here: brainly.com/question/25770607
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Answer:
cos 37=x/b (second one)
sin 37= a/b (third one)
tan 37=a/x (sixth one)
Step-by-step explanation:
Cos is defined by the adjacent side over the hypotenuse. Cos 37 would be x/b. Clearly, that is option 2. Sin is defined by opposite over hypotenuse. Sin 37 would be a/b. That is the 3rd option. Tan is defined by opposite over adjacent. Tan 37 would be a/x or the 6th option.
Answer:
x = -1 and y = -1
Step-by-step explanation:
Solve 3x+3y=−6;−x+y=0
Steps:
I will solve your system by substitution.
−x+y=0;3x+3y=−6
Step: Solve−x+y=0for y:
−x+y+x=0+x(Add x to both sides)
y=x
Step: Substitutexforyin3x+3y=−6:
3x+3y=−6
3x+3x=−6
6x=−6(Simplify both sides of the equation)
6x
6
=
−6
6
(Divide both sides by 6)
x=−1
Step: Substitute−1forxiny=x:
y=x
y=−1
Answer:
x=−1 and y=−1
1.1 Factoring: 4x2+9y2+16z2-6xy-12yz-8xz
Thoughtfully split the expression at hand into groups, each group having two terms :
Group 1: -6xy-12yz
Group 2: 16z2-8xz
Group 3: 4x2+9y2
Pull out from each group separately :
Group 1: (x+2z) • (-6y)
Group 2: (x-2z) • (-8z)
Group 3: (4x2+9y2) • (1)
Looking for common sub-expressions :
Group 1: (x+2z) • (-6y)
Group 3: (4x2+9y2) • (1)
Group 2: (x-2z) • (-8z)
